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%I #44 Aug 02 2022 13:02:04
%S 0,0,12,200,2280,22420,205212,1806000,15522960,131383340,1100093412,
%T 9138243400,75445046040,619838752260,5072272077612,41371548418400,
%U 336519691295520,2730963319321180,22119245290765812,178854325039467000,1444135501669535400
%N Number of 3-way interactions when 3 subsets of power set on {1..n} are chosen at random; number of Boolean functions of n variables and rank 3 from Post class F(8,inf).
%D W. W. Kokko, "Interactions", manuscript, 1983.
%H Vincenzo Librandi, <a href="/A036240/b036240.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Jovovic and G. Kilibarda, <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=dm&paperid=398&option_lang=eng">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
%H Thomas Wieder, <a href="http://www.math.nthu.edu.tw/~amen/2008/070301.pdf">The number of certain k-combinations of an n-set</a>, Applied Mathematics Electronic Notes, vol. 8 (2008).
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (25,-241,1135,-2734,3160,-1344).
%F a(n) = (8^n-7^n-3*4^n+3*3^n+2*2^n-2)/6.
%F G.f.: 4*x^3*(43*x^2-25*x+3) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(7*x-1)*(8*x-1)). - _Colin Barker_, Dec 10 2012
%F a(n) = 25*a(n-1)-241*a(n-2)+1135*a(n-3)-2734*a(n-4)+3160*a(n-5)-1344*a(n-6). - _Wesley Ivan Hurt_, Oct 23 2014
%F E.g.f.: exp(x)*(exp(x) - 1)^3*(exp(x) + 1)^2*(exp(2*x) + 2)/6. - _Stefano Spezia_, Jul 29 2022
%p A036240:=n->(8^n-7^n-3*4^n+3*3^n+2*2^n-2)/6: seq(A036240(n), n=1..30); # _Wesley Ivan Hurt_, Oct 23 2014
%t CoefficientList[Series[4 x^2 (43 x^2 - 25 x + 3)/((x - 1) (2 x - 1) (3 x - 1) (4 x - 1) (7 x - 1) (8 x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)
%t LinearRecurrence[{25,-241,1135,-2734,3160,-1344},{0,0,12,200,2280,22420},30] (* _Harvey P. Dale_, Dec 29 2013 *)
%o (PARI) a(n) = (1/3!)*(8^n-7^n-3*4^n+3*3^n+2*2^n-2); \\ _Joerg Arndt_, Oct 21 2013
%o (Magma) [(8^n-7^n-3*4^n+3*3^n+2*2^n-2)/6 : n in [1..30]]; // _Wesley Ivan Hurt_, Oct 23 2014
%Y Cf. A036239.
%K nonn,easy,nice
%O 1,3
%A _N. J. A. Sloane_
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